What is the integral from 0 to 7 of (9x-x^2)-(2x) ?

The integral from 0 to 7 of (9x-x^2)-(2x) is 343/6

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integral from 0 to 7 of (9x-x^2)-(2x)

\int_{0}^{7} (9 x - x^{2}) - (2 x) d x

\frac{343}{6}

Decimal

57.16666 \dots

Solution steps

\int_{0}^{7} 9 x - x^{2} - 2 x d x

Simplify

= \int_{0}^{7} - x^{2} + 7 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{0}^{7} x^{2} d x + \int_{0}^{7} 7 x d x

\int_{0}^{7} x^{2} d x = \frac{343}{3}

\int_{0}^{7} 7 x d x = \frac{343}{2}

= - \frac{343}{3} + \frac{343}{2}

Simplify

- \frac{343}{3} + \frac{343}{2} : \frac{343}{6}

= \frac{343}{6}

\frac{0.01 s}{7 s ^{2} + 19980}

\frac{d}{d x} (\frac{- ln ( 1 - 6 x )}{x})

\frac{d}{d x} (x^{e} + e^{x})

\frac{d}{d x} (7 x y)

\frac{d}{d x} (arcsec (2 x + 1))

What is the integral from 0 to 7 of (9x-x^2)-(2x) ?
The integral from 0 to 7 of (9x-x^2)-(2x) is 343/6